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A brute force approach to find multipliers for the first part of Peter Winkler's math puzzle 'Zeros, ones or twos', in his book _Mathematical Puzzles_
# A horrible awful brute-force approach to Peter Winkler's 'Zeroes, ones and twos' problem, part 1
(1..100).each do |p|
found = false
q = 0
until found
q += 1
product = p * q
if !(product.to_s =~ /[^01]/) || q > 1000000000
found = true
p "#{p} * #{q} = #{product}"
end
end
end
# A slightly less brute-force approach to Peter Winkler's 'Zeroes, ones and twos' problem, part 1
# this time it only checks each multiplier for the remaining undiscovered numbers
require 'pp'
pairs = {}
my_range = (1..1000)
partners = my_range.to_a
q = 0
until partners.empty? || q > 100000000000
q += 1
hits , misses = partners.partition {|p| !((p * q).to_s =~ /[^01]/)}
hits.each do |p|
pairs[p]=[q,p*q]
p "#{pairs.length}: #{p} * #{q} = #{p*q}"
end
partners = misses
end
pp pairs.sort
@Vaguery
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Vaguery commented Feb 22, 2019

And the smallest k, such that n*k contains only even digits:

[[1, [2, 2]],
 [2, [1, 2]],
 [3, [2, 6]],
 [4, [1, 4]],
 [5, [4, 20]],
 [6, [1, 6]],
 [7, [4, 28]],
 [8, [1, 8]],
 [9, [32, 288]],
 [10, [2, 20]],
 [11, [2, 22]],
 [12, [2, 24]],
 [13, [2, 26]],
 [14, [2, 28]],
 [15, [4, 60]],
 [16, [3, 48]],
 [17, [4, 68]],
 [18, [16, 288]],
 [19, [12, 228]],
 [20, [1, 20]],
 [21, [2, 42]],
 [22, [1, 22]],
 [23, [2, 46]],
 [24, [1, 24]],
 [25, [8, 200]],
 [26, [1, 26]],
 [27, [18, 486]],
 [28, [1, 28]],
 [29, [14, 406]],
 [30, [2, 60]],
 [31, [2, 62]],
 [32, [2, 64]],
 [33, [2, 66]],
 [34, [2, 68]],
 [35, [8, 280]],
 [36, [8, 288]],
 [37, [6, 222]],
 [38, [6, 228]],
 [39, [12, 468]],
 [40, [1, 40]],
 [41, [2, 82]],
 [42, [1, 42]],
 [43, [2, 86]],
 [44, [1, 44]],
 [45, [64, 2880]],
 [46, [1, 46]],
 [47, [6, 282]],
 [48, [1, 48]],
 [49, [14, 686]],
 [50, [4, 200]],
 [51, [4, 204]],
 [52, [4, 208]],
 [53, [8, 424]],
 [54, [9, 486]],
 [55, [4, 220]],
 [56, [4, 224]],
 [57, [4, 228]],
 [58, [7, 406]],
 [59, [14, 826]],
 [60, [1, 60]],
 [61, [4, 244]],
 [62, [1, 62]],
 [63, [14, 882]],
 [64, [1, 64]],
 [65, [4, 260]],
 [66, [1, 66]],
 [67, [4, 268]],
 [68, [1, 68]],
 [69, [12, 828]],
 [70, [4, 280]],
 [71, [4, 284]],
 [72, [4, 288]],
 [73, [28, 2044]],
 [74, [3, 222]],
 [75, [8, 600]],
 [76, [3, 228]],
 [77, [6, 462]],
 [78, [6, 468]],
 [79, [34, 2686]],
 [80, [1, 80]],
 [81, [6, 486]],
 [82, [1, 82]],
 [83, [8, 664]],
 [84, [1, 84]],
 [85, [8, 680]],
 [86, [1, 86]],
 [87, [24, 2088]],
 [88, [1, 88]],
 [89, [32, 2848]],
 [90, [32, 2880]],
 [91, [22, 2002]],
 [92, [5, 460]],
 [93, [22, 2046]],
 [94, [3, 282]],
 [95, [24, 2280]],
 [96, [3, 288]],
 [97, [44, 4268]],
 [98, [7, 686]],
 [99, [2312, 228888]],
 [100, [2, 200]],
 [101, [2, 202]],
 [102, [2, 204]],
 [103, [2, 206]],
 [104, [2, 208]],
 [105, [4, 420]],
 [106, [4, 424]],
 [107, [4, 428]],
 [108, [6, 648]],
 [109, [74, 8066]],
 [110, [2, 220]],
 [111, [2, 222]],
 [112, [2, 224]],
 [113, [2, 226]],
 [114, [2, 228]],
 [115, [4, 460]],
 [116, [4, 464]],
 [117, [4, 468]],
 [118, [7, 826]],
 [119, [34, 4046]],
 [120, [2, 240]],
 [121, [2, 242]],
 [122, [2, 244]],
 [123, [2, 246]],
 [124, [2, 248]],
 [125, [16, 2000]],
 [126, [7, 882]],
 [127, [18, 2286]],
 [128, [5, 640]],
 [129, [16, 2064]],
 [130, [2, 260]],
 [131, [2, 262]],
 [132, [2, 264]],
 [133, [2, 266]],
 [134, [2, 268]],
 [135, [36, 4860]],
 [136, [3, 408]],
 [137, [6, 822]],
 [138, [6, 828]],
 [139, [16, 2224]],
 [140, [2, 280]],
 [141, [2, 282]],
 [142, [2, 284]],
 [143, [2, 286]],
 [144, [2, 288]],
 [145, [28, 4060]],
 [146, [14, 2044]],
 [147, [6, 882]],
 [148, [3, 444]],
 [149, [14, 2086]],
 [150, [4, 600]],
 [151, [4, 604]],
 [152, [4, 608]],
 [153, [16, 2448]],
 [154, [3, 462]],
 [155, [4, 620]],
 [156, [3, 468]],
 [157, [4, 628]],
 [158, [17, 2686]],
 [159, [14, 2226]],
 [160, [3, 480]],
 [161, [4, 644]],
 [162, [3, 486]],
 [163, [14, 2282]],
 [164, [5, 820]],
 [165, [4, 660]],
 [166, [4, 664]],
 [167, [4, 668]],
 [168, [5, 840]],
 [169, [12, 2028]],
 [170, [4, 680]],
 [171, [4, 684]],
 [172, [4, 688]],
 [173, [14, 2422]],
 [174, [12, 2088]],
 [175, [16, 2800]],
 [176, [5, 880]],
 [177, [24, 4248]],
 [178, [16, 2848]],
 [179, [16, 2864]],
 [180, [16, 2880]],
 [181, [48, 8688]],
 [182, [11, 2002]],
 [183, [22, 4026]],
 [184, [11, 2024]],
 [185, [12, 2220]],
 [186, [11, 2046]],
 [187, [12, 2244]],
 [188, [11, 2068]],
 [189, [12, 2268]],
 [190, [12, 2280]],
 [191, [22, 4202]],
 [192, [14, 2688]],
 [193, [22, 4246]],
 [194, [22, 4268]],
 [195, [24, 4680]],
 [196, [33, 6468]],
 [197, [44, 8668]],
 [198, [1156, 228888]],
 [199, [112, 22288]],
 [200, [1, 200]],
 [201, [2, 402]],
 [202, [1, 202]],
 [203, [2, 406]],
 [204, [1, 204]],
 [205, [4, 820]],
 [206, [1, 206]],
 [207, [4, 828]],
 [208, [1, 208]],
 [209, [32, 6688]],
 [210, [2, 420]],
 [211, [2, 422]],
 [212, [2, 424]],
 [213, [2, 426]],
 [214, [2, 428]],
 [215, [4, 860]],
 [216, [3, 648]],
 [217, [4, 868]],
 [218, [37, 8066]],
 [219, [12, 2628]],
 [220, [1, 220]],
 [221, [2, 442]],
 [222, [1, 222]],
 [223, [2, 446]],
 [224, [1, 224]],
 [225, [128, 28800]],
 [226, [1, 226]],
 [227, [18, 4086]],
 [228, [1, 228]],
 [229, [36, 8244]],
 [230, [2, 460]],
 [231, [2, 462]],
 [232, [2, 464]],
 [233, [2, 466]],
 [234, [2, 468]],
 [235, [12, 2820]],
 [236, [18, 4248]],
 [237, [12, 2844]],
 [238, [17, 4046]],
 [239, [12, 2868]],
 [240, [1, 240]],
 [241, [2, 482]],
 [242, [1, 242]],
 [243, [2, 486]],
 [244, [1, 244]],
 [245, [28, 6860]],
 [246, [1, 246]],
 [247, [18, 4446]],
 [248, [1, 248]],
 [249, [18, 4482]],
 [250, [8, 2000]],
 [251, [8, 2008]],
 [252, [9, 2268]],
 [253, [8, 2024]],
 [254, [9, 2286]],
 [255, [8, 2040]],
 [256, [8, 2048]],
 [257, [18, 4626]],
 [258, [8, 2064]],
 [259, [18, 4662]],
 [260, [1, 260]],
 [261, [8, 2088]],
 [262, [1, 262]],
 [263, [16, 4208]],
 [264, [1, 264]],
 [265, [16, 4240]],
 [266, [1, 266]],
 [267, [18, 4806]],
 [268, [1, 268]],
 [269, [18, 4842]],
 [270, [18, 4860]],
 [271, [82, 22222]],
 [272, [9, 2448]],
 [273, [22, 6006]],
 [274, [3, 822]],
 [275, [8, 2200]],
 [276, [3, 828]],
 [277, [24, 6648]],
 [278, [8, 2224]],
 [279, [16, 4464]],
 [280, [1, 280]],
 [281, [8, 2248]],
 [282, [1, 282]],
 [283, [8, 2264]],
 [284, [1, 284]],
 [285, [8, 2280]],
 [286, [1, 286]],
 [287, [24, 6888]],
 [288, [1, 288]],
 [289, [14, 4046]],
 [290, [14, 4060]],
 [291, [22, 6402]],
 [292, [7, 2044]],
 [293, [16, 4688]],
 [294, [3, 882]],
 [295, [28, 8260]],
 [296, [3, 888]],
 [297, [838, 248886]],
 [298, [7, 2086]],
 [299, [134, 40066]],
 [300, [2, 600]],
 [301, [2, 602]],
 [302, [2, 604]],
 [303, [2, 606]],
 [304, [2, 608]],
 [305, [8, 2440]],
 [306, [8, 2448]],
 [307, [66, 20262]],
 [308, [8, 2464]],
 [309, [72, 22248]],
 [310, [2, 620]],
 [311, [2, 622]],
 [312, [2, 624]],
 [313, [2, 626]],
 [314, [2, 628]],
 [315, [28, 8820]],
 [316, [9, 2844]],
 [317, [26, 8242]],
 [318, [7, 2226]],
 [319, [14, 4466]],
 [320, [2, 640]],
 [321, [2, 642]],
 [322, [2, 644]],
 [323, [2, 646]],
 [324, [2, 648]],
 [325, [8, 2600]],
 [326, [7, 2282]],
 [327, [186, 60822]],
 [328, [8, 2624]],
 [329, [14, 4606]],
 [330, [2, 660]],
 [331, [2, 662]],
 [332, [2, 664]],
 [333, [2, 666]],
 [334, [2, 668]],
 [335, [8, 2680]],
 [336, [8, 2688]],
 [337, [6, 2022]],
 [338, [6, 2028]],
 [339, [12, 4068]],
 [340, [2, 680]],
 [341, [2, 682]],
 [342, [2, 684]],
 [343, [2, 686]],
 [344, [2, 688]],
 [345, [24, 8280]],
 [346, [7, 2422]],
 [347, [6, 2082]],
 [348, [6, 2088]],
 [349, [14, 4886]],
 [350, [8, 2800]],
 [351, [8, 2808]],
 [352, [7, 2464]],
 [353, [8, 2824]],
 [354, [12, 4248]],
 [355, [8, 2840]],
 [356, [8, 2848]],
 [357, [12, 4284]],
 [358, [8, 2864]],
 [359, [18, 6462]],
 [360, [8, 2880]],
 [361, [8, 2888]],
 [362, [24, 8688]],
 [363, [68, 24684]],
 [364, [11, 4004]],
 [365, [56, 20440]],
 [366, [11, 4026]],
 [367, [6, 2202]],
 [368, [6, 2208]],
 [369, [12, 4428]],
 [370, [6, 2220]],
 [371, [6, 2226]],
 [372, [7, 2604]],
 [373, [22, 8206]],
 [374, [6, 2244]],
 [375, [16, 6000]],
 [376, [13, 4888]],
 [377, [6, 2262]],
 [378, [6, 2268]],
 [379, [16, 6064]],
 [380, [6, 2280]],
 [381, [6, 2286]],
 [382, [11, 4202]],
 [383, [22, 8426]],
 [384, [7, 2688]],
 [385, [12, 4620]],
 [386, [11, 4246]],
 [387, [12, 4644]],
 [388, [11, 4268]],
 [389, [12, 4668]],
 [390, [12, 4680]],
 [391, [22, 8602]],
 [392, [17, 6664]],
 [393, [16, 6288]],
 [394, [22, 8668]],
 [395, [68, 26860]],
 [396, [578, 228888]],
 [397, [52, 20644]],
 [398, [56, 22288]],
 [399, [112, 44688]],
 [400, [1, 400]],
 [401, [2, 802]],
 [402, [1, 402]],
 [403, [2, 806]],
 [404, [1, 404]],
 [405, [12, 4860]],
 [406, [1, 406]],
 [407, [6, 2442]],
 [408, [1, 408]],
 [409, [54, 22086]],
 [410, [2, 820]],
 [411, [2, 822]],
 [412, [2, 824]],
 [413, [2, 826]],
 [414, [2, 828]],
 [415, [16, 6640]],
 [416, [5, 2080]],
 [417, [64, 26688]],
 [418, [16, 6688]],
 [419, [54, 22626]],
 [420, [1, 420]],
 [421, [2, 842]],
 [422, [1, 422]],
 [423, [2, 846]],
 [424, [1, 424]],
 [425, [16, 6800]],
 [426, [1, 426]],
 [427, [52, 22204]],
 [428, [1, 428]],
 [429, [14, 6006]],
 [430, [2, 860]],
 [431, [2, 862]],
 [432, [2, 864]],
 [433, [2, 866]],
 [434, [2, 868]],
 [435, [48, 20880]],
 [436, [19, 8284]],
 [437, [6, 2622]],
 [438, [6, 2628]],
 [439, [52, 22828]],
 [440, [1, 440]],
 [441, [2, 882]],
 [442, [1, 442]],
 [443, [2, 886]],
 [444, [1, 444]],
 [445, [64, 28480]],
 [446, [1, 446]],
 [447, [6, 2682]],
 [448, [1, 448]],
 [449, [14, 6286]],
 [450, [64, 28800]],
 [451, [64, 28864]],
 [452, [5, 2260]],
 [453, [54, 24462]],
 [454, [9, 4086]],
 [455, [44, 20020]],
 [456, [5, 2280]],
 [457, [18, 8226]],
 [458, [18, 8244]],
 [459, [14, 6426]],
 [460, [1, 460]],
 [461, [44, 20284]],
 [462, [1, 462]],
 [463, [14, 6482]],
 [464, [1, 464]],
 [465, [44, 20460]],
 [466, [1, 466]],
 [467, [6, 2802]],
 [468, [1, 468]],
 [469, [18, 8442]],
 [470, [6, 2820]],
 [471, [6, 2826]],
 [472, [9, 4248]],
 [473, [14, 6622]],
 [474, [6, 2844]],
 [475, [48, 22800]],
 [476, [9, 4284]],
 [477, [6, 2862]],
 [478, [6, 2868]],
 [479, [18, 8622]],
 [480, [1, 480]],
 [481, [6, 2886]],
 [482, [1, 482]],
 [483, [42, 20286]],
 [484, [1, 484]],
 [485, [88, 42680]],
 [486, [1, 486]],
 [487, [46, 22402]],
 [488, [1, 488]],
 [489, [14, 6846]],
 [490, [14, 6860]],
 [491, [42, 20622]],
 [492, [5, 2460]],
 [493, [54, 26622]],
 [494, [9, 4446]],
 [495, [4624, 2288880]],
 [496, [5, 2480]],
 [497, [46, 22862]],
 [498, [9, 4482]],
 [499, [134, 66866]],
 [500, [4, 2000]],
 [501, [4, 2004]],
 [502, [4, 2008]],
 [503, [8, 4024]],
 [504, [12, 6048]],
 [505, [4, 2020]],
 [506, [4, 2024]],
 [507, [4, 2028]],
 [508, [8, 4064]],
 [509, [52, 26468]],
 [510, [4, 2040]],
 [511, [4, 2044]],
 [512, [4, 2048]],
 [513, [16, 8208]],
 [514, [9, 4626]],
 [515, [4, 2060]],
 [516, [4, 2064]],
 [517, [4, 2068]],
 [518, [9, 4662]],
 [519, [12, 6228]],
 [520, [4, 2080]],
 [521, [4, 2084]],
 [522, [4, 2088]],
 [523, [54, 28242]],
 [524, [5, 2620]],
 [525, [8, 4200]],
 [526, [8, 4208]],
 [527, [38, 20026]],
 [528, [5, 2640]],
 [529, [16, 8464]],
 [530, [8, 4240]],
 [531, [8, 4248]],
 [532, [5, 2660]],
 [533, [8, 4264]],
 [534, [9, 4806]],
 [535, [8, 4280]],
 [536, [5, 2680]],
 [537, [12, 6444]],
 [538, [9, 4842]],
 [539, [12, 6468]],
 [540, [9, 4860]],
 [541, [46, 24886]],
 [542, [41, 22222]],
 [543, [16, 8688]],
 [544, [42, 22848]],
 [545, [148, 80660]],
 [546, [11, 6006]],
 [547, [44, 24068]],
 [548, [11, 6028]],
 [549, [38, 20862]],
 [550, [4, 2200]],
 [551, [4, 2204]],
 [552, [4, 2208]],
 [553, [8, 4424]],
 [554, [12, 6648]],
 [555, [4, 2220]],
 [556, [4, 2224]],
 [557, [4, 2228]],
 [558, [8, 4464]],
 [559, [72, 40248]],
 [560, [4, 2240]],
 [561, [4, 2244]],
 [562, [4, 2248]],
 [563, [36, 20268]],
 [564, [5, 2820]],
 [565, [4, 2260]],
 [566, [4, 2264]],
 [567, [4, 2268]],
 [568, [5, 2840]],
 [569, [12, 6828]],
 [570, [4, 2280]],
 [571, [4, 2284]],
 [572, [4, 2288]],
 [573, [14, 8022]],
 [574, [12, 6888]],
 [575, [8, 4600]],
 [576, [5, 2880]],
 [577, [84, 48468]],
 [578, [7, 4046]],
 [579, [36, 20844]],
 [580, [7, 4060]],
 [581, [8, 4648]],
 [582, [11, 6402]],
 [583, [8, 4664]],
 [584, [7, 4088]],
 [585, [8, 4680]],
 [586, [8, 4688]],
 [587, [72, 42264]],
 [588, [11, 6468]],
 [589, [14, 8246]],
 [590, [14, 8260]],
 [591, [42, 24822]],
 [592, [14, 8288]],
 [593, [48, 28464]],
 [594, [419, 248886]],
 [595, [68, 40460]],
 [596, [34, 20264]],
 [597, [38, 22686]],
 [598, [67, 40066]],
 [599, [114, 68286]],
 [600, [1, 600]],
 [601, [4, 2404]],
 [602, [1, 602]],
 [603, [8, 4824]],
 [604, [1, 604]],
 [605, [4, 2420]],
 [606, [1, 606]],
 [607, [4, 2428]],
 [608, [1, 608]],
 [609, [76, 46284]],
 [610, [4, 2440]],
 [611, [4, 2444]],
 [612, [4, 2448]],
 [613, [34, 20842]],
 [614, [33, 20262]],
 [615, [4, 2460]],
 [616, [4, 2464]],
 [617, [4, 2468]],
 [618, [36, 22248]],
 [619, [14, 8666]],
 [620, [1, 620]],
 [621, [4, 2484]],
 [622, [1, 622]],
 [623, [36, 22428]],
 [624, [1, 624]],
 [625, [32, 20000]],
 [626, [1, 626]],
 [627, [32, 20064]],
 [628, [1, 628]],
 [629, [14, 8806]],
 [630, [14, 8820]],
 [631, [106, 66886]],
 [632, [7, 4424]],
 [633, [14, 8862]],
 [634, [13, 8242]],
 [635, [36, 22860]],
 [636, [13, 8268]],
 [637, [38, 24206]],
 [638, [7, 4466]],
 [639, [32, 20448]],
 [640, [1, 640]],
 [641, [44, 28204]],
 [642, [1, 642]],
 [643, [76, 48868]],
 [644, [1, 644]],
 [645, [32, 20640]],
 [646, [1, 646]],
 [647, [44, 28468]],
 [648, [1, 648]],
 [649, [34, 22066]],
 [650, [4, 2600]],
 [651, [4, 2604]],
 [652, [4, 2608]],
 [653, [34, 22202]],
 [654, [93, 60822]],
 [655, [4, 2620]],
 [656, [4, 2624]],
 [657, [4, 2628]],
 [658, [7, 4606]],
 [659, [34, 22406]],
 [660, [1, 660]],
 [661, [4, 2644]],
 [662, [1, 662]],
 [663, [122, 80886]],
 [664, [1, 664]],
 [665, [4, 2660]],
 [666, [1, 666]],
 [667, [4, 2668]],
 [668, [1, 668]],
 [669, [12, 8028]],
 [670, [4, 2680]],
 [671, [4, 2684]],
 [672, [4, 2688]],
 [673, [34, 22882]],
 [674, [3, 2022]],
 [675, [72, 48600]],
 [676, [3, 2028]],
 [677, [6, 4062]],
 [678, [6, 4068]],
 [679, [36, 24444]],
 [680, [1, 680]],
 [681, [6, 4086]],
 [682, [1, 682]],
 [683, [42, 28686]],
 [684, [1, 684]],
 [685, [12, 8220]],
 [686, [1, 686]],
 [687, [12, 8244]],
 [688, [1, 688]],
 [689, [12, 8268]],
 [690, [12, 8280]],
 [691, [62, 42842]],
 [692, [7, 4844]],
 [693, [388, 268884]],
 [694, [3, 2082]],
 [695, [32, 22240]],
 [696, [3, 2088]],
 [697, [38, 26486]],
 [698, [7, 4886]],
 [699, [118, 82482]],
 [700, [4, 2800]],
 [701, [4, 2804]],
 [702, [4, 2808]],
 [703, [94, 66082]],
 [704, [6, 4224]],
 [705, [4, 2820]],
 [706, [4, 2824]],
 [707, [4, 2828]],
 [708, [6, 4248]],
 [709, [32, 22688]],
 [710, [4, 2840]],
 [711, [4, 2844]],
 [712, [4, 2848]],
 [713, [34, 24242]],
 [714, [6, 4284]],
 [715, [4, 2860]],
 [716, [4, 2864]],
 [717, [4, 2868]],
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